[search] using OR and NOT in solr query

Putting together comments from a couple different answers here, in the Solr docs and on the other SO question, I found that the following syntax produces the correct result for my use case

(my_field=my_value or my_field is null):

(my_field:"my_value" OR (*:* NOT my_field:*))

This works for solr 4.1.0. This is slightly different than the use case in the OP; but, I thought that others would find it useful.